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Theorem bj-nnst 13318
Description: Double negation of stability of a formula. Intuitionistic logic refutes unstability (but does not prove stability) of any formula. This theorem can also be proved in classical refutability calculus (see set.mm/bj-peircestab) but not in minimal calculus (see set.mm/bj-stabpeirce). (Contributed by BJ, 9-Oct-2019.)
Assertion
Ref Expression
bj-nnst  |-  -.  -. STAB  ph

Proof of Theorem bj-nnst
StepHypRef Expression
1 nndc 837 . 2  |-  -.  -. DECID  ph
2 dcstab 830 . . 3  |-  (DECID  ph  -> STAB  ph )
32con3i 622 . 2  |-  ( -. STAB  ph  ->  -. DECID  ph )
41, 3mto 652 1  |-  -.  -. STAB  ph
Colors of variables: wff set class
Syntax hints:   -. wn 3  STAB wstab 816  DECID wdc 820
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-io 699
This theorem depends on definitions:  df-bi 116  df-stab 817  df-dc 821
This theorem is referenced by:  bj-dcst  13321  bj-stst  13322
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